Just checking open circuit voltage won't tell you much about the condition of a battery. A load test will probably confirm the hydrometer readings. What were the actual readings and do you have access to a load tester?
An accurate hydrometer will tell you the 'state of charge' of each individual cell...and all the cells should read close to the same 'reading'...if you have one or more cells much 'lower' than the others, you most likely have battery that needs to be replaced...
If you are charging a 'low' battery, a hydrometer is the best way to monitor the progress of the charging process, and will indicate when the battery is fully charged...if you leave the battery at rest for about 24 hours, and check the cells with the hydrometer again, finding they are all close in their readings, you're set to go...
A voltmeter, on the other hand, will usually only give you rough indication of the battery's condition or state of charge...
Voltmeter readings should be done with a Digital meter, for accuracy...and should only be used to measure the 'state of charge' if the battery has been at rest for a day or so, without any charging or discharging...a battery right off the charger won't give you a meaningful voltmeter reading - it will most always read as 'good'...let the battery rest, then read the voltage...
If your 'charged' battery shows a voltage of around 10 volts the day after charging, you have a 'shorted' cell, IE, a 10 volt battery, and your 12 volt charging system will overcharge the good cells causing heat and bubbling of the acid solution, and most likely that rotten egg smell...time to replace the battery, for sure!...Caution here, as the hydrogen gas being emitted can be very dangerous if you set off a spark nearby....BOOM...remember to ALWAYS turn OFF the charger BEFORE removing the charging leads from the battery posts..
A voltmeter is a fairly cheap way for mfg's to help users monitor the battery system's performance...it's too bad they won't spend a bit more to install some LED's in the monitor panel that would indicate when the charger is in the 'bulk', 'finishing' for 'float' modes so we'd know when the batteries are charged enough to shut down the generator!
Second Roamer Short answer is "YES" happens often in fact
NOTE on Hydrometers.. There are two or 3 kinds
1: Temperature compensated. These are the very best, and most accurate way of finding out a battery's state of charge
2: Non Temperature compensated. You need a chart with these, you read the temp and the specific gravity, then look up the compensated value on the chart, equally accurate, but a whole lot more work to use
3; El-cheapo.. Like the floating ball types.. .... JUNK for the most part, but they can give you an indication
NOTE on Hydrometer use.. One of the issues that is covered by equalization of a battery is stratification.. Stratification is where the fluid on top is near pure water (Specific gravity 1.0) but the fluid farther down is... .Acid (Heavier) and thus you get a false "Dead" reading with the hydrometer. Just so you know
Agitation (Which equalization provides) corrects this